Cryptanalysis on prime power RSA modulus of the form N=prq

Let $N = p^r q$ be an RSA prime power modulus for $r \geq 2$ and $q < p < 2 q$. This paper propose three new attacks. In the first attack we consider the class of public exponents satisfying an equation $e X - N Y = u p^r + \frac{q^r}{u} + Z$ for suitably small positive integer $u$. Using continued fraction we show that $\frac{Y}{X}$ can be recovered among the convergents of the continued fraction expansion of $\frac{e}{N}$ and leads to the successful factorization of $N p^r q$. Moreover we show that the number of such exponents is at least $N^{\frac{r+3}{2(r+1)}-\varepsilon}$ where $\varepsilon \geq 0$ is arbitrarily small for large $N$. The second and third attacks works when $k$ RSA public keys $(N_i,e_i)$ are such that there exist $k$ relations of the shape $e_i x - N_i y_i = p_i^r u + \frac{q_i^r}{u} + z_i$ or of the shape $e_i x_i - N_i y = p_i^r u + \frac{q_i^r}{u} + z_i$ where the parameters $x$, $x_i$, $y$, $y_i$, $z_i$ are suitably small in terms of the prime factors of the moduli. We apply the LLL algorithm, and show that our strategy enable us to simultaneously factor the $k$ prime power RSA moduli $N_i$

New attacks on prime power N = prq using good approximation of φ(N)

This paper proposes three new attacks. Our first attack is based on the RSA key equation ed − kφ(N) = 1 where φ(N) = pr-1(p-1)(q-1). Let q <p <2q and 2p 3r+2/r+1 |p r-1/r+1 – q r-1/r+1| < 1/6Ny with d = Nδ. If δ < 1-y/2 we shows that k/d can be recovered among the convergents of the continued fractions expansions of e/N-2N r/r+1 + N r-1/r+1. We furthered our analysis on j prime power moduli Ni = priqi satisfying a variant of the above mentioned condition. We utilized the LLL algorithm on j prime power public keys (Ni, ei) with Ni = priqi and we were able to factorize the j prime power moduli Ni = priqi simultaneously in polynomial time

Public key exponent attacks on multi-prime power modulus using continued fraction expansion method

This paper proposes three public key exponent attacks of breaking the security of the prime power modulus =22 where and are distinct prime numbers of the same bit size. The first approach shows that the RSA prime power modulus =22 for q&lt;&lt;2q using key equation −()=1 where ()= 22(−1)(−1) can be broken by recovering the secret keys&nbsp; / from the convergents of the continued fraction expansion of e/−23/4 +1/2 . The paper also reports the second and third approaches of factoring multi-prime power moduli =2 2 simultaneously through exploiting generalized system of equations −()=1 and −()=1 respectively. This can be achieved in polynomial time through utilizing Lenstra Lenstra Lovasz (LLL) algorithm and simultaneous Diophantine approximations method for =1,2,…,

The Profile and Significance of Listed Property Companies in Some Selected African Countries

This study investigates the significance and profile of Listed Property Companies (LPCs) in 10 African countries namely; Botswana, Egypt, Kenya, Mauritius, Morocco, Nigeria, South Africa, Tunisia, Zambia, and Zimbabwe respectively for the period of 10 years from 2006 to 2015., the profile and some key indicators of each respective country has been identified to determine the significance of each respective economy. The study uses secondary data obtained from Thompson Reuters DataStream to extract the number of companies in each country and their respective profiles. Descriptive statistics were used to analyze 64 Listed Property Companies using simple percentages. The study revealed that most of the African countries are Opaque with very few semi-transparent such as Kenya, Mauritius, and Botswana with the exception of South Africa which is the only transparent, the study further revealed that most of the companies are established between 2010 to 2015. Egypt has the highest number of property companies 29 represented by 45.31 % followed by South Africa with 16 Listed property Companies Represented by 25 % while Nigeria, Kenya and Zambia have the least number of companies with 1 each represented by 1.56%

An assessment of corporate social responsibility of property developers in Bauchi Metropolis, Nigeria

Purpose: The study aims to assess the corporate social responsibility of property developers in Bauchi metropolis with a view to examine the importance and effects of corporate social responsibility on property development in the study area. This study is limited to Bauchi metropolis. Research Methodology:The study uses descriptive and exploratory research design using quantitative research approach.&nbsp;Questionnaires were administered to 20 property developers within Bauchi metropolis using purposive sampling techniques. Reliability was investigated by an overall average Cronbach’s Alpha value of 0.81, the data obtained was analyzed using percentage computation, weighted mean, relative importance index (RII) and severity index (SI) were also used. Findings: The most important corporate social responsibility (CSR) to the property developers is environmental sustainability followed by a qualitative environment, the less important is the safety of houses. Furthermore, the highest CSR provided by the developers is environmental sustainability. Among the highest effects of neglecting corporate social responsibility is causing damage to the environment while the least is developing poor neighborhoods. Limitations: This study explored on only 20 property development firms within Bauchi metropolis, results might not necessarily apply to other firms within the metropolis. Contribution: This study will be of significant importance to the government and professional bodies in the built environment in terms of policy formulation, these can help checkmate the property development companies in carrying out corporate social responsibilities to the immediate environment they operate thereby becoming socially responsible and allowing the general public/community to enjoy projects that will enhance their lives. Keywords:Corporate social responsibility, Sustainable development, property developer

Assessment of Selected Health Determinants among Almajiri Students in Gwadabawa Local Government, Sokoto State, Nigeria

Health determinants are factors that can influence our health either positively or negatively. This paper determined the factors that affect the health of Almajiri in their system of study in Gwadabawa local government of Sokoto state, Nigeria. Interview and visual observation were used to collect data, which was analyzed by thematic networks method. The result of this study was shown. Most (50.0%) of the Almajiri live in buildings own by school,whereas, 33.5% of them in donated buildings .There were three types of houses / classes where Almajiri live.Most (50.0%) were made of cement/modern style ,then (33.3%) the mud houses / classes, and (16.7%) were the ones from zinc .There were toilets for urination only ,no one was slated for defecation . In 75% of the schools there was no water, whereas 33.3% have water source from unprotected wells. In 33.3 % of the schools there was refuse dumps .In 33.3% there were no any source of risk. Whereas, in 16.7% there were gutters, and in 16.7% there were roads nearby. Personal hygiene was observed. 75.0% of Almajiri wore dirty garments.25.0% wore cleaned garments, 12.5% wore torn garments, and 87.5% wore untorn garments. 62.5% wore shoes and 37.5% have no shoes. 62.5% take bath weekly, 37.7% take bath daily. Interms of livelihood, most of them relied on begging for food; 25.0% do domestic work to get food and other needs. 70.0% of them eat twice in a day, 25.0% thrice, whereas, 5.0% once; in most cases. The result revealed many health determinants which can negatively affect the health of Almajiri.Keywords: health determinants, open defecation, overcrowding, begging, child labou

Purification characterization and inhibition studies on Phospholipase C from Opisthacanthus capensis (Black Scorpion) venom

Phospholipase C from Opisthacanthus capensis venom was partially purified and characterized. The enzyme was purified 105.2 fold with an overall yield of 13% using various purification steps involving ammonium sulphate precipitation, protamine sulphate treatment, sephadex G-75  fractionation and DE-52 anion exchange chromatography. The purified enzyme was  homogeneous with a molecular weight of 29 kDa. The  phospholipase C has pH and temperature optima of 7.2 and 600C, respectively with activation energy of 25KJ/mol and t1/2 of 1.50 hr. Initial velocity studies on O. capensis venom phospholipase C revealed a KM of 0.02 mM and Vmax of 0.015 μmol/min. Studies on the effect of pH on KM and Vmax gave PKa1 of 6.9 and PKa2 of 7.4 with enthalpy of ionization of 20 KJ/mol suggesting  histidine in the active site. The enzyme was positively modulated by Mg2+, Zn2+ and Ca2+ and negatively by Fe2+. While Hg2+ produced complete inhibition. Various concentrations of leaf aqueous extract of Momordica charantia also inhibited the activity of O. capensis venom phospholipase C in vitro with a competitive pattern. This study revealed the presence of phospholipase C in O. capensis venom and gave some scientific basis for the use of theplant in the treatment of scorpion envenomation.Keywords: Phospholipase C; Opisthacanthus capensis;  Momordica charantia; Veno

Construction of Finite Cellular Automata Using the (123) - Avoiding Class of Aunu Permutation Pattern Application: In Game Of Chance

Abstract: It was shown in Sadiq (2013

Global Retinoblastoma Presentation and Analysis by National Income Level.

Importance: Early diagnosis of retinoblastoma, the most common intraocular cancer, can save both a child's life and vision. However, anecdotal evidence suggests that many children across the world are diagnosed late. To our knowledge, the clinical presentation of retinoblastoma has never been assessed on a global scale. Objectives: To report the retinoblastoma stage at diagnosis in patients across the world during a single year, to investigate associations between clinical variables and national income level, and to investigate risk factors for advanced disease at diagnosis. Design, Setting, and Participants: A total of 278 retinoblastoma treatment centers were recruited from June 2017 through December 2018 to participate in a cross-sectional analysis of treatment-naive patients with retinoblastoma who were diagnosed in 2017. Main Outcomes and Measures: Age at presentation, proportion of familial history of retinoblastoma, and tumor stage and metastasis. Results: The cohort included 4351 new patients from 153 countries; the median age at diagnosis was 30.5 (interquartile range, 18.3-45.9) months, and 1976 patients (45.4%) were female. Most patients (n = 3685 [84.7%]) were from low- and middle-income countries (LMICs). Globally, the most common indication for referral was leukocoria (n = 2638 [62.8%]), followed by strabismus (n = 429 [10.2%]) and proptosis (n = 309 [7.4%]). Patients from high-income countries (HICs) were diagnosed at a median age of 14.1 months, with 656 of 666 (98.5%) patients having intraocular retinoblastoma and 2 (0.3%) having metastasis. Patients from low-income countries were diagnosed at a median age of 30.5 months, with 256 of 521 (49.1%) having extraocular retinoblastoma and 94 of 498 (18.9%) having metastasis. Lower national income level was associated with older presentation age, higher proportion of locally advanced disease and distant metastasis, and smaller proportion of familial history of retinoblastoma. Advanced disease at diagnosis was more common in LMICs even after adjusting for age (odds ratio for low-income countries vs upper-middle-income countries and HICs, 17.92 [95% CI, 12.94-24.80], and for lower-middle-income countries vs upper-middle-income countries and HICs, 5.74 [95% CI, 4.30-7.68]). Conclusions and Relevance: This study is estimated to have included more than half of all new retinoblastoma cases worldwide in 2017. Children from LMICs, where the main global retinoblastoma burden lies, presented at an older age with more advanced disease and demonstrated a smaller proportion of familial history of retinoblastoma, likely because many do not reach a childbearing age. Given that retinoblastoma is curable, these data are concerning and mandate intervention at national and international levels. Further studies are needed to investigate factors, other than age at presentation, that may be associated with advanced disease in LMICs